Effects of a finite axial magnetic field on the beam loading of a cavity

The effect of a finite axial magnetic field on the beam loading of a cavity is evaluated. The calculation extends Branch's classic paper on ballistic bunching in that both the conductive and susceptive components of the beam-loaded admittance are computed, for general values of axial magnetic field. Also included is a comparison of the analytic formulation with a two-dimensional particle-in-cell simulation. This paper suggests that the finite axial magnetic field used in linear beam tubes (typically exceeding 1.5 x the Brillouin field) would only modify the beam-loaded admittance by about 20%, from that computed under the assumption of an infinite axial magnetic field.